WVTransformBarotropicQG

A transform for modeling single-layer quasigeostrophic flow

Declaration

classdef WVTransformBarotropicQG < WVTransform

Overview

This is a two-dimensional, single-layer which may be interpreted as the sea-surface height. The ‘h’ parameter is the equivalent depth, and 0.80 m is a typical value for the first baroclinic mode.

Lxy = 50e3;
Nxy = 256;
latitude = 25;
wvt = WVTransformSingleMode([Lxy, Lxy], [Nxy, Nxy], h=0.8, latitude=latitude);

Topics

Initialization
- WVTransformBarotropicQG create geometry for 2D barotropic flow
Domain attributes
- Spatial grid
  - Lx length of the x-dimension
  - Ly length of the y-dimension
  - Nx number of grid points in the x-dimension
  - Ny number of grid points in the y-dimension
  - fastTransform fast transform object
  - x dimension
  - y dimension
- DFT grid
  - Nk_dft length of the k-wavenumber dimension on the DFT grid
  - Nl_dft length of the l-wavenumber dimension on the DFT grid
  - conjugateDimension assumed conjugate dimension
  - kMode_dft k mode-number on the DFT grid
  - k_dft k wavenumber dimension on the DFT grid
  - lMode_dft l mode-number on the DFT grid
  - l_dft l wavenumber dimension on the DFT grid
- WV grid
  - Nkl length of the combined kl-wavenumber dimension on the WV grid
  - dftConjugateIndex index into the DFT grid of the conjugate of each WV mode
  - dftConjugateIndices2D index into the DFT grid of the conjugate of each WV mode
  - dftPrimaryIndex index into the DFT grid of each WV mode
  - dftPrimaryIndices2D index into the DFT grid of each WV mode
  - dk wavenumber spacing of the \(k\) axis
  - dl wavenumber spacing of the \(l\) axis
  - k wavenumber dimension on the WV grid
  - kMode_wv k mode number on the WV grid
  - kRadial radial (k,l) wavenumber on the WV grid
  - kl wavenumber dimension
  - l wavenumber dimension on the WV grid
  - lMode_wv l mode number on the WV grid
  - shouldAntialias whether the WV grid includes quadratically aliased wavenumbers
  - shouldExcludeNyquist whether the WV grid includes Nyquist wavenumbers
  - shouldExludeConjugates whether the WV grid includes wavenumbers that are Hermitian conjugates
  - wvConjugateIndex index into the WV mode that matches the dftConjugateIndices
Initial conditions
- Geostrophic Motions
  - initWithGeostrophicStreamfunction initialize with a geostrophic streamfunction
  - setGeostrophicStreamfunction set a geostrophic streamfunction
  - addGeostrophicStreamfunction add a geostrophic streamfunction to existing geostrophic motions
  - setGeostrophicModes set amplitudes of the given geostrophic modes
  - addGeostrophicModes add amplitudes of the given geostrophic modes
  - removeAllGeostrophicMotions remove all geostrophic motions
Utility function
- degreesOfFreedomForComplexMatrix a matrix with the number of degrees-of-freedom at each entry
- degreesOfFreedomForRealMatrix a matrix with the number of degrees-of-freedom at each entry
- indicesOfFourierConjugates a matrix of linear indices of the conjugate
- isHermitian Check if the matrix is Hermitian. Report errors.
- setConjugateToUnity set the conjugate of the wavenumber (iK,iL) to 1
Properties
- effectiveHorizontalGridResolution returns the effective grid resolution in meters
Primary flow components
- geostrophicComponent returns the geostrophic flow component
Energetics
- geostrophicEnergy total energy of the geostrophic flow
- geostrophicKineticEnergy kinetic energy of the geostrophic flow
- geostrophicPotentialEnergy potential energy of the geostrophic flow
Index gymnastics
- indexFromKLModeNumber return the linear index into k_wv and l_wv from a mode number
- indicesFromDFTGridToWVGrid indices to convert from DFT to WV grid
- indicesFromWVGridToDFTGrid indices to convert from WV to DFT grid
- indicesFromWVGridToFFTWGrid indices to convert from WV to DFT grid
- isValidConjugateKLModeNumber return a boolean indicating whether (k,l) is a valid conjugate WV mode number
- isValidKLModeNumber return a boolean indicating whether (k,l) is a valid WV mode number
- isValidPrimaryKLModeNumber return a boolean indicating whether (k,l) is a valid primary (non-conjugate) WV mode number
- klModeNumberFromIndex return mode number from a linear index into a WV matrix
- primaryKLModeNumberFromKLModeNumber takes any valid WV mode number and returns the primary mode number
Masks
- maskForAliasedModes returns a mask with locations of modes that will alias with a quadratic multiplication.
- maskForConjugateFourierCoefficients a mask indicate the components that are redundant conjugates
- maskForNyquistModes returns a mask with locations of modes that are not fully resolved
Developer
- propertyAnnotationsForGeometry return array of CAPropertyAnnotations initialized by default
Operations
- Grid transformation
  - transformFromDFTGridToWVGrid convert from DFT to WV grid
  - transformFromWVGridToDFTGrid convert from a WV to DFT grid
- Fourier transformation
  - transformFromSpatialDomainToDFTGrid transform from \((x,y,z)\) to \((k,l,z)\) on the DFT grid
  - transformToSpatialDomainFromDFTGrid transform from \((k,l,z)\) on the DFT grid to \((x,y,z)\)
  - transformToSpatialDomainFromDFTGridAtPosition transform from \((k,l)\) on the DFT grid to \((x,y)\) at any position
- Transformations
  - transformToKLAxes transforms in the spectral domain from (j,kl) to (kAxis,lAxis,j)
  - transformToRadialWavenumber transforms in the spectral domain from (j,kl) to (j,kRadial)
Other
- A0N
- A0Z
- F0
- Fpv
- J
- K
- K2
- Kh
- L
- Lr2
- Lz
- NA0
- Nj
- PA0
- UA0
- VA0
- X
- Y
- Z
- beta
- classRequiredPropertyNames
- diffX
- diffY
- effectiveJMax
- enstrophyFluxFromF0
- f
- fluxForForcing
- g
- geometryFromFile
- geometryFromGroup
- h
- h_0 [Nj 1]
- indexFromModeNumber
- inertialPeriod
- j
- kAxis
- klGrid
- kljGrid
- lAxis
- latitude
- maxFg
- modeNumberFromIndex
- namesOfRequiredPropertiesForGeometry
- namesOfRequiredPropertiesForRotatingFPlane
- namesOfRequiredPropertiesForTransform
- namesOfTransformVariables
- newNonrequiredPropertyNames
- newRequiredPropertyNames
- planetaryRadius
- propertyAnnotationsForRotatingFPlane
- qgpvFluxFromF0
- requiredPropertiesForGeometryFromGroup This guy ignores Nz, because we will just use the default
- requiredPropertiesForRotatingFPlaneFromGroup
- requiredPropertiesForTransformFromGroup
- rotationRate
- setSSH
- spatialMatrixSize
- spectralMatrixSize
- totalEnstrophy
- totalEnstrophySpatiallyIntegrated
- transformFromGroup
- transformFromSpatialDomainWithFourier
- transformQGPVToWaveVortex
- transformToSpatialDomainWithFourier
- transformToSpatialDomainWithFourierAtPosition
- xyGrid